Dimethyl phthalate, diethyl phthalate, dibutyl phthalate, and dioctyl phthalate series samples were measured by the reed-vibration mechanical spectroscopy for liquids recently invented. The results indicate that the processes of dynamical glass transition, crystallization of the supercooled liquid, crystal-liquid phase transition, and gasification take place successively for the dimethyl phthalate sample in the measured temperature range on heating, but only the glass transition and the gasification appear in the other 3 samples. The above measurements and corresponding analysis show that the reed-vibration mechanical spectroscopy for liquids is a reliable and effective method for the investigation of physical processes in liquid state, so that it could provide physical information of soft condensed matter.